Question

If $k>0$ and the product of the roots of the equation $x^2-3kx+2e^{2{\log }_{e}k}-1=0$ is 7, then the sum of the roots is

• A. $2$
• B. $4$
• C. $6$
• D. $8$

Answer 1

The correct option is C $6$

$x^2-3kx+{2e}^{2\log k}-1=0$
$x^2-3kx+2k^2-1=0$
$\alpha \beta =7\dots \dots$(1)
$\alpha \beta =2k^2-1\dots \dots$(2)
$\alpha +\beta =3k$
$2k^2-1=7$ (from equation (1) and (2))
$k=\pm 2$
$k=2$ ($\because k>0$)
$\alpha +\beta =6$